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Bit-interleaved coded modulation with iterative decoding (BICM-ID) offers improved error performance over additive white Gaussian noise and fading channels if it uses a wisely designed signal mapping. Furthermore, error performance of BICM-ID can be significantly improved by employing multi-dimensional (MD) modulation. However, suitable MD mappings are obtained by computer search techniques, except for MD modulations that use small constellations, e.g., binary phase shift keying, quadrature phase shift keying, and 8-ary phase shift keying as basic modulation. The alphabet size of MD modulations increases exponentially as the order of the basic modulation increases and computer searching becomes intractable. In this paper, we propose a systematic mapping method for MD modulations. The innovation of our proposed method is that it generates MD mappings using 16- and 64-quadrature amplitude modulation very efficiently. The presented numerical results show that the proposed method improves the bit error rate of BICM-ID.

Efficient Multi-Dimensional Mapping Using QAM Constellations for BICM-ID